Sums and Arithmetic Series Quick Questions

Question

Jenny decides to raise money for her local charity by encouraging people to lay quarters on the floor of a classroom in the shape of an equilateral triangle. She puts one quarter in the first row, two in the second, three in the third, and so on. Her target is to raise $400. How many rows does she need ?

i had 400/2 (2(1)+(400-1)1)= 80,200... I feel like that's too high of a number though ... ?

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write the sum using sigma notation

2) 30+25+20+15+10+5

----i got £ 2 on top and k=7 on bottom ---> 5k-5 .... Is it possible to start from 7 and go down to 2 ? Because in all my problems we start from a low number and go up ? Hope it makes sense ? (pretend this £ is the sigma sign)

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how would you simplify 

3) ((25rad2)/2) (rad2 +25rad2)

4) 0.5/2 (26.5+0.5) 

THANK YOU !!!!!

 

Answer 1

Sarah,

 

The first part is a Fibonacci sequence where:

1=(1*2)/2

1+2=(2*3)/2

1+2+3=(3*4)/2

That means to get 400 we need:

n(n+1)/2=400

n(n+1)=200

 

Now we can guess approximately what n is.

Ex. n=11: 11*12/2=66

n=20: 20*21/2=210

n=30: 30*31/2=465. Too much.l

n=26: 26*27/2=365. too few.

n=28: 28*29/2=406. Almost there!

n=27: 27*28/2=378. too few.

So you need 28 rows.

 

To write a sum in decreasing order you express it as 30-5k from k=0 to 5.

 

To simplify things with radicals of 2, you need to multiply through with radicals of 2. So in this case you would multiply each term with radical of 2, making it:

(25*2/2)(2+25*2)=25(52)

 

Hope that helps,

Deanna